Question: If $x \triangleleft y = 4x^{2}-y^{2}$ and $x \bigtriangledown y = x+6y$, find $(-6 \bigtriangledown 1) \triangleleft -3$.
Solution: First, find $-6 \bigtriangledown 1$ $ -6 \bigtriangledown 1 = -6+(6)(1)$ $ \hphantom{-6 \bigtriangledown 1} = 0$ Now, find $0 \triangleleft -3$ $ 0 \triangleleft -3 = 4(0^{2})-(-3)^{2}$ $ \hphantom{0 \triangleleft -3} = -9$.